Pre set-up
Import libraries
library(reshape2)
library(ggplot2)
library(plotly)
library(plyr)
library(Rfast)
library(data.table)
library(knitr)
library(rstudioapi)
Import own functions
# Get path current script is in
source_path = dirname(rstudioapi::getSourceEditorContext()$path)
# Source functions required for this script
source(file.path(source_path, 'Beta_pseudo_sim.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'Gaussian_pseudo_sim.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'Create_design.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'Create_miniblock.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'PE_dep_LR_choice_model.R', fsep = .Platform$file.sep))
Parameter set-up
Set up reward space
# Reward lower and upper boundary
reward_space_lb = 1
reward_space_ub = 100
# Set up space for plotting
reward_space_length = 1000
reward_space = seq(reward_space_lb,
reward_space_ub,
length=reward_space_length)
Gaussian parameters and distribution
# Parameters
gaussian_mean = (100 * 1/6) * 3
gaussian_sd = (100 * 1/6) / 3
# Distribution
gaussian_densities = dnorm(reward_space, gaussian_mean, gaussian_sd)
# Normalize density
gaussian_densities = scale(gaussian_densities) - min(scale(gaussian_densities))
Beta parameters and distributions
# Set up "skewdness" parameter for easier change of slope
beta_skewedness = 5
# Parameters for lower end beta and upper end beta
beta_a_le = beta_skewedness/3
beta_b_le = 2*beta_skewedness/3
beta_a_ue = 2*beta_skewedness/3
beta_b_ue = beta_skewedness/3
# Create distributions
beta_densities_le = dbeta(seq(0,1,length=reward_space_length), beta_a_le,beta_b_le)
beta_densities_ue = dbeta(seq(0,1,length=reward_space_length), beta_a_ue,beta_b_ue)
# Normalize densities
beta_densities_le = scale(beta_densities_le) - min(scale(beta_densities_le))
beta_densities_ue = scale(beta_densities_ue) - min(scale(beta_densities_le))
Set rare event threshold
# Set rare events to be 20% of the sampled data
rare_lim = 0.2
Control plots
Plot distributions
# Form data frame from density values
data_densities = data.frame(reward_space,
gaussian_densities,
beta_densities_le,
beta_densities_ue)
# Bring data frame into long format
data_densities = melt(data_densities, id.vars='reward_space')
# Disribution plot
p_dist = ggplot(data=data_densities, aes(x=reward_space, y=value, group=as.factor(variable),
color=as.factor(variable))) +
geom_line(size=1) +
scale_color_brewer(palette='Accent') +
scale_x_continuous(limits = c(1,100)) +
#stat_summary(fun.data = 'mean', geom = 'vline') +
geom_vline(xintercept=c(1/3, 1/2, 2/3)*100, linetype='dashed', alpha=0.5, size=0.1) +
labs(title='Density functions of used distributions',
x='Outcome',
y='Normalized density',
color='Distributions') +
theme(plot.title=element_text(size=15, face='bold', hjust=0.5),
axis.title=element_text(size=12))
p_dist

Test sampling with histograms
# Define parameters
n_samples = 500
data_sampling = data.frame(c(1:n_samples))
colnames(data_sampling) = 'Sample'
# Fill data frame with samples
data_sampling$stim_1 = Beta_pseudo_sim(n_samples, beta_a_le, beta_b_le, 'b_le',
reward_space_lb, reward_space_ub)$outcome
data_sampling$stim_2 = Gaussian_pseudo_sim(n_samples, gaussian_mean, gaussian_sd, 'g_an',
reward_space_lb, reward_space_ub)$outcome
data_sampling$stim_3 = Beta_pseudo_sim(n_samples, beta_a_ue, beta_b_ue, 'b_ue',
reward_space_lb, reward_space_ub)$outcome
data_sampling = melt(data_sampling, id.vars='Sample')
# Plot histograms
p_sampling = ggplot(data=data_sampling, aes(x=value, fill=variable)) +
scale_fill_brewer(palette = 'Accent') +
geom_histogram(binwidth = 1) +
facet_wrap(~variable)
ggplotly(p_sampling)
Simulating data for the choice model
---
title: "Simulation PE dependent LR"
output: html_notebook
---

# Pre set-up

### Import libraries
```{r}
library(reshape2)
library(ggplot2)
library(plotly)
library(plyr)
library(Rfast)
library(data.table)
library(knitr)
library(rstudioapi)
```


### Import own functions
```{r}
# Get path current script is in
source_path = dirname(rstudioapi::getSourceEditorContext()$path)
# Source functions required for this script
source(file.path(source_path, 'Beta_pseudo_sim.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'Gaussian_pseudo_sim.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'Create_design.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'Create_miniblock.R', fsep = .Platform$file.sep))
source(file.path(source_path, 'PE_dep_LR_choice_model.R', fsep = .Platform$file.sep))
```

# Parameter set-up

### Set up reward space
```{r}
# Reward lower and upper boundary
reward_space_lb = 1
reward_space_ub = 100

# Set up space for plotting
reward_space_length = 1000
reward_space = seq(reward_space_lb, 
                   reward_space_ub,
                   length=reward_space_length)
```

### Gaussian parameters and distribution
```{r}
# Parameters
gaussian_mean = (100 * 1/6) * 3
gaussian_sd = (100 * 1/6) / 3

# Distribution
gaussian_densities = dnorm(reward_space, gaussian_mean, gaussian_sd)
# Normalize density
gaussian_densities = scale(gaussian_densities) - min(scale(gaussian_densities))
```

### Beta parameters and distributions
```{r}
# Set up "skewdness" parameter for easier change of slope
beta_skewedness = 5
# Parameters for lower end beta and upper end beta
beta_a_le = beta_skewedness/3
beta_b_le = 2*beta_skewedness/3
beta_a_ue = 2*beta_skewedness/3
beta_b_ue = beta_skewedness/3
# Create distributions
beta_densities_le = dbeta(seq(0,1,length=reward_space_length), beta_a_le,beta_b_le)
beta_densities_ue = dbeta(seq(0,1,length=reward_space_length), beta_a_ue,beta_b_ue)
# Normalize densities
beta_densities_le = scale(beta_densities_le) - min(scale(beta_densities_le))
beta_densities_ue = scale(beta_densities_ue) - min(scale(beta_densities_le))
```

### Set rare event threshold
```{r}
# Set rare events to be 20% of the sampled data
rare_lim = 0.2
```

---

# Control plots

### Plot distributions
```{r out.width='100%', warning=FALSE}
# Form data frame from density values
data_densities = data.frame(reward_space, 
                            gaussian_densities,
                            beta_densities_le,
                            beta_densities_ue)

# Bring data frame into long format
data_densities = melt(data_densities, id.vars='reward_space')

# Disribution plot
p_dist = ggplot(data=data_densities, aes(x=reward_space, y=value, group=as.factor(variable),
                                    color=as.factor(variable))) +
  geom_line(size=1) +
  scale_color_brewer(palette='Accent') +
  scale_x_continuous(limits = c(1,100)) +
  #stat_summary(fun.data = 'mean', geom = 'vline') +
  geom_vline(xintercept=c(1/3, 1/2, 2/3)*100, linetype='dashed', alpha=0.5, size=0.1) +
  labs(title='Density functions of used distributions',
       x='Outcome',
       y='Normalized density',
       color='Distributions') +
  theme(plot.title=element_text(size=15, face='bold', hjust=0.5),
        axis.title=element_text(size=12))

p_dist
```

### Test sampling with histograms
```{r out.width='100%', warning=FALSE}
# Define parameters
n_samples = 500
data_sampling = data.frame(c(1:n_samples))
colnames(data_sampling) = 'Sample'

# Fill data frame with samples
data_sampling$stim_1 = Beta_pseudo_sim(n_samples, beta_a_le, beta_b_le, 'b_le',
                                       reward_space_lb, reward_space_ub)$outcome
data_sampling$stim_2 = Gaussian_pseudo_sim(n_samples, gaussian_mean, gaussian_sd, 'g_an',
                                           reward_space_lb, reward_space_ub)$outcome
data_sampling$stim_3 = Beta_pseudo_sim(n_samples, beta_a_ue, beta_b_ue, 'b_ue',
                                       reward_space_lb, reward_space_ub)$outcome
data_sampling = melt(data_sampling, id.vars='Sample')

# Plot histograms
p_sampling = ggplot(data=data_sampling, aes(x=value, fill=variable)) +
  scale_fill_brewer(palette = 'Accent') +
  geom_histogram(binwidth = 1) +
  facet_wrap(~variable)

ggplotly(p_sampling)
```

---

### Simulating data for the choice model

```{r echo=FALSE}
# Define simulation parameters
n_subjects = 40
subjects = c(1:n_subjects)
n_miniblocks = 25
alpha0 = 0.3
alpha1 = 0.6
temperature = 7

# Set up matrix to store data in (to append subjects)
data_model = matrix(0,0,17)

# Loop over each subject
for(sub_count in subjects){
  # Simulate data for subject
  design = Create_design(n_miniblocks,
                         beta_a_le,
                         beta_b_le,
                         gaussian_mean,
                         gaussian_sd,
                         beta_a_ue,
                         beta_b_ue,
                         reward_space_lb,
                         reward_space_ub)
  
  # Create matrix to store data for each subject
  results = matrix(0,nrow(design),ncol(data_model))
  results[,1] = subjects[sub_count]
  results[,2] = c(1:nrow(design))
  results[,3] = design$option_left
  results[,4] = design$option_right
  results[,5] = design$reward_stim_1
  results[,6] = design$reward_stim_2
  results[,7] = design$comp_number


  # Run model over simulated data
  sim = PE_dep_LR_choice_model(design, alpha0, alpha1, temperature)
  # Save model values, PE and fPE for ech trial and subject into matrix
  results[,8] = sim$choice$choice
  results[,9:11] = as.matrix(sim$values)
  results[,12:14] = as.matrix(sim$PE)
  results[,15:17] = as.matrix(sim$fPE)

  # Append all subjects
  data_model = rbind(data_model, results)
}

# Convert to data frame (How our data will look like in the study)
data_model = data.frame(data_model)
colnames(data_model) = c('sub_id', 'trial', 'stim_1', 'stim_2',
                         'reward_stim_1', 'reward_stim_2', 'comp_number', 'choice',
                        'v_stim_1', 'v_stim_2', 'v_stim_3',
                        'pe_stim_1', 'pe_stim_2', 'pe_stim_3',
                        'fpe_stim_1', 'fpe_stim_2', 'fpe_stim_3')
# Sort after participants
data_model = data_model[order(data_model$sub_id),]
```

